Finite Group DatabasebetaFinite Group Databasebeta| order | 1920 |
| isoclinism | isoclinic class of C5⋊#85645 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3 · Schur multiplier (H2) = C25 |
| unambiguous semidirect product | C5⋊#85645 |
| Fitting, derived | C26×C5 ⋊ C2×C3 |
| Hall | C22×#4099 ⋊ C3 |
| Sylow | C5 ⋊ #85645 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C1 | G |
| commutator, Fitting, cosocle, hypocenter | C26×C5 | C2×C3 |
| Frattini | C22 | D5×C22⋊A4 |
| socle | C24×C5 | C2×A4 |
| LCS | G ▷ C26×C5 | |
| UCS | C1 | |
1648 conjugacy classes of subgroups; only the 34 normal subgroups are shown.
This group has 1648 conjugacy classes of subgroups — too many to draw. Only its 34 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 120 |
Polycyclic presentation:
2,3,2^6,5|e^a=eg,f^a=fgh,i^a=i^4,c^b=cd,d^b=c,e^b=ef,f^b=e,g^b=h,h^b=gh72 conjugacy classes — view the full character table.
| maximal subgroup of | D5×#85645 |
| maximal normal subgroup of | D5×#85645 |
| maximal quotient of | #72253500 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1920, 239966);